With the known method a stretchable foil that is welded completely together at one end is gathered in accordion-like folds and set on rod-shaped holder elements such as gathering fingers of a tensioning frame. Then the holder elements are moved apart so that the stretchable foil is prestretched transversely. In this condition the stretching frame is moved downward along the object stack and if necessary over any pallet carrying the stack and the gathered foil is fitted against the outside of the stack and if necessary on the pallet carrying the stack. The gathering fingers can also be formed as gathering wedges, each gathering wedge being comprised of a horizontally oriented and angled tube section. The gathering wedges are oriented on the corners of the stack and are movable along lines extending through the middle of the stack to the respective corners.
A disadvantage is that the weld seam at the welded-together end that comes to rest on the top of the stack forms two large triangular upwardly projecting points. These points reach into the corners of the stack. This means on the one hand that quite a bit of foil is used. In addition these points must in a further step either be adhered to the sides or top of the stack so that the wrapped stack has a neat appearance and the points do not get in the way during transport. Adhering the points reduces the amount of printable space on the package. In addition water can get between the adhered points and be held there, something that is not wanted.